Ryan Clark Calls Sean Payton a Thug

Sean Payton is also not a HC who doesn't like to bend or "tinker" with his offensive philosophy or have the patience to work with talented, skilled, but kind of raw, unconventional, improvisational QB's like Brett Favre, Steve Young were and how Mike Holmgren, and Bill Walsh/George Seifert adapted to their styles and fit them in perfectly within their offensive systems.
But he totally "bent" his philosophy for Drew. Sean Payton has a (Mid)West Coast background and built up a Coryell based offense for Drew since that is what he ran in San Diego. He builds his offense to the strength of the QB. The problem with Russ is skillset wise, he was, as has always been limited and I think that because of the success he had, he . I said something to the effect a few years ago that he would probably have the "Taysom" playbook.

For 90-95% of the time, especially when it came to how effective, overwhelmingly powerful, and potent our offenses were during their respective primes from 2006-13. After the 2013 season, although Brees' had more then a few great statistical seasons and our offenses in succeeding seasons still were very good and could score at will sometimes, and Payton had to do a post-Bountygate, mini-rebuild by 2017, both Brees' and Payton best years were behind them because a lot of the great offensive players (Moore, Colston, Henderson, Sproles) were either gone, retired, or been traded.

Sometimes, Brees said or nixed some of Payton's offensive plays he sent in or audibled it or changed the design, aspects of the plays so it might better increase its chances of succeeding. Brees' had the aura, hard-earned street and professional cred, all-around respect and reputation to tell Payton what Russell Wilson, other QB's he's worked with from his days as Giants QB coach/OC under Jim Fassell can't or aren't allowed to and that's "No". And get away it, too.

Bill Parcells once said you have to have one equally strong-willed, personality whether its QB or assistant OCA, to calm Payton down or maybe modify or alter slightly some of his play-calling, or offensive philosophy. He won't like it perhaps, in fact he might hate you for it for a while, but eventually he'll come around regarding most circumstances if he realizes it makes his job easier or his offenses more effective and productive. When Sean begins calling plays based more around the logical reasoning his over-inflated ego tells him it'll work as opposed to statistical in-game situational analysis, problems usually tend to pop up.
Mastery of the system. You said it best; he gotten enough respect from Payton to be able to have command of the offense in that manner. But it did take time to get there.